The presently disclosed subject matter generally relates to energy efficiency, and more particularly to optimized harvesting of energy from relatively low frequency sources, for other effective uses. In some instances, harvested energy may be obtained in optimized fashion from ambient sound sources in sufficient amounts for use to power circuits or to be stored for subsequent use.
In the present-day digital economy, recent advancements in low power electronics, micro-electromechanical systems, wireless sensors, and electronic gadgets have significantly increased daily power demands. Increased use of cell phones, tablets, and other devices such as iPods or iPads throughout the world has resulted in a surprisingly high energy footprint, with one recent report claiming that household energy demand has increased by 3.4% since 1990. Based on calculations just for use in the United States, smart phone usage is estimated to demand 1,269,000 Wh of energy per year (International Energy Agency). It is considered that power demands could be significantly alleviated if much of such demands of power can be satisfied by local powering devices, such as harvesting energy from abundant ambient noises, a renewable form of energy. Accordingly, different local energy harvesters have been proposed using multiple micro-cantilevers to scavenge energies from various alternate sources.
Some energy harvesters utilize the ability of piezoelectric materials to generate electric potential in response to external mechanical deformations. Some efforts have sought to achieve in essence self-powered wireless electronics such that maintenance, replacement of old batteries, and chemical waste from conventional batteries could be avoided. Various low power energy harvesters have been provided for such purposes. Micro-cantilever energy harvesters are one known form of low power energy harvesters with power outputs in the range of microwatts.
More recently, plate-type energy harvesters for high-frequency applications have been proposed. Conventional energy harvesters, using the physics of structural resonance to harvest dynamic energy, require dimensions or a footprint to be on the order of few times higher than the wavelength of the excitation frequencies. Therefore, miniature cantilever energy harvesters have been often designed for high-frequency applications.
Due to size limitations at lower frequencies, fewer solutions have sought use of the physics of phononic crystals (PCs). PCs offer the ability to introduce novel wave traveling and wave filtering phenomena within the structure and its structural constituents. PCs can create frequency band gaps through Bragg scattering or through local resonances. Such band gaps are frequency intervals in which the elastic waves are incapable of propagating through the material due to the interference of the waves, caused by the impedance mismatch in the periodic geometry or the material discontinuities. At such band gaps or at the band of resonance frequencies, the filtered wave energy gets localized in the structure which could be further utilized to harvest energy from the PCs. Accordingly, some approaches have introduced PCs for harvesting energy.
One researcher has proposed a method of guiding waves through an acoustic funnel to a metamaterial energy harvester that uses a parabolic acoustic mirror. Hexagonally oriented PCs with piezoelectric-coated cantilever beams at each joint have been proposed for a grid energy harvester, though such approaches were proposed to harvest energies from relatively higher frequencies, such as above about 50 kHz.
Concerning possibilities more focused on harvesting energies at relatively lower acoustic frequencies (for example, of about less than 1 kHz), the physics have been significantly altered, such as introducing a cavity in the PC to localize the acoustic energy at the resonance frequencies while the energy was harvested using polyvinylidene fluoride (PVDF) film. Power output from such low-frequency PC-based energy harvesters has been quite low (in the range of nanowatts (nW) or a few microwatts (mW) against 10 KOhm load resistance.
One researcher has reported a model that could harvest considerably higher electric potential using a one-dimensional (1D) phononic piezoelectric cantilever beam. Instead of arresting the local resonance phenomenon, Bragg scattering physics was employed to harvest energy. While efficient energy harvesting was achieved, the model length could be too large (1 m long) to power small electronic devices if the energy has to be harvested below about 1 kHz. Also, such small-scale harvesters based on the physics of PCs were limited to harvesting energy only at a single frequency.
Since acoustoelastic sonic crystal (AESC) devices possess similar phenomena like PCs (though using different physics) and are capable of introducing local resonance modes, an AESC could be a better choice over PC harvesters for some circumstances. AESCs can be considered as a spring-mass combination in a mass-in-mass system. Per some prior work, an AESC can be provided as a composite material composed of soft and stiff components.
One prior approach has used an AESC structural unit consisting of a square mass connected to a square frame by four convolute folded beams. Upon unit excitation, a maximum of 0.005 V (approximately, power output in nW range against reference load resistance) could be harvested, which is a relatively low amount.
Also previously, an acoustoelastic metamaterial-based energy harvester has been proposed which is capable of harvesting energy at relatively low acoustic frequencies (about 3 kHz) using sub-wavelength scale geometry. Such harvester demonstrated the ability to harvest energy at a specific frequency from a unit-cell model. However, possibilities to scavenge energy at other frequencies within the low frequency limit were not specified.
Another prior approach has sought to advance AESC energy harvester which is able to simultaneously addresses five principal targets:
1. Harvest energy below about 1 kHz, that is, at Hz level;
2. Predictively control model geometry;
3. Harvest energy at multiple frequencies;
4. Show ability to harvest energy by both displacement and acoustic pressure excitation; and
5. Output higher power density close to 100 mW/cm2.
AESCs may be used to stop acoustic wave propagation at a particular frequency. Using a mass-in-mass system, low-frequency stop band filters are designed to filter wave energy at local resonance frequencies trapped inside a soft constituent of the sonic crystal as dynamic strain energy. It is possible to recover the same energy using embedded piezoelectric wafers (lead zirconate titanate, “PZT”). Prior art FIG. 1 represents the use of an AESC energy scavenger generally 10 exposed to an ambient vibration acoustic noise environment generally 12, which contains broadband frequencies. In AESC 10, the soft material is used as a host matrix to house the heavier mass. Power is harvested when the local resonance of the embedded mass strains the soft composite matrix which is recovered by the embedded piezoelectric wafers such as representative wafer 14.
Local resonance is key to wave filtration (as generally represented at 16) for creation of a band stop for certain frequencies, and for harvesting energy from the AESC model (as generally represented at 18). Dispersion curve and density of states (DOS) of the unit-cell AESC are calculated to find the possible local resonance modes less than 1 kHz frequency. Strategic PZT placement and loading conditions further the scavenging of power at those local resonance frequencies. With such an arrangement, it is possible to localize the energy at multiple low frequencies, to be harvested through appropriate PZT design and placement.
For testing both the controlled displacement and the pressure wave excitation, the exemplary device may be vibrated harmonically using a shacking base for displacement excitation, while the structures may be excited using acoustic pressure or noise to test a pressure wave mechanism. Such testing confirmed capability of the AESC structure to perform simultaneous wave filtration and energy harvesting.
FIG. 2A illustrates a prior art three-dimensional unit-cell acoustic metamaterial comprising a rectangular 1.43″×1.43″×0.55″ (3.65 cm×3.65 cm×1.4 cm) prism generally 20. Such prism 20 as illustrated comprises rectangular aluminum frame 22 housing a cylindrical soft rubber (matrix) material 24. A spherical heavy lead core 26 is encapsulated into the matrix material 24, where diameters of the core 26 and the matrix are 0.49″ (12.5 mm) and 0.98″ (25 mm), respectively. Stiffness (Young's modulus) for aluminum, lead, and rubber are 68.9 GPa, 13.5 GPa, and 0.98 MPa, respectively.
Piezoelectric disc generally 28 is embedded into the matrix material 24, in between lead core 26 and inner aluminum wall 22, to convert strain energy into electric potential at local resonance.
The unit-cell model of the metamaterial generally 20 could be exhibited as conventional one-dimensional spring-mass system, as represented in prior art FIG. 2B. For calculation purposes, one may assume that displacement of the masses follow the time-harmonic wave behavior, similar to that of the applied force, i.e., F(t)=Re({circumflex over (F)}e−iωt). Acknowledging the equation of motion and balancing the linear momentum of the system, dynamic effective mass of the microstructure is shown by Equation 1, herein, as below:
                              M          eff                =                              M            0                    +                                    2              ⁢                              Km                1                                                                    2                ⁢                K                            -                                                m                  1                                ⁢                                  ω                                      2                    ⁢                                                                                                                                              +                                    2              ⁢                              Km                2                                                                    2                ⁢                K                            -                                                m                  2                                ⁢                                  ω                  2                                                                                        (                  Equation          ⁢                                          ⁢          1                )            where M0, m1 and m2 are the masses of aluminum frame 22, lead core 26, and PZT 28, respectively. K represents the spring constant for the rubber component.
Assuming thickness-polarized piezoelectric state and ignoring effects from other directions, the piezoelectric charge density displacement is given by Equation 2 herein, as below:D3=d33T3+ε33E3   (Equation 2)where T3 is the total compressive stress acted on PZT. ε33 (=1500*8.854 pF/m), d33 (=593 pm/V) and E3 are the permittivity, piezoelectric charge constant and electric field strength, respectively, in the thickness direction.
Following assumptions, dynamic output potential and Frequency Response Function (FRF) are obtained per Equations 3-7, as follows:
                                          V            0                    ⁡                      (            ω            )                          =                              i            ⁢                                                  ⁢            ω            ⁢                                                  ⁢                          C              1                        ⁢                          R              0                        ⁢                          U              0                                            1            -                          i              ⁢                                                          ⁢              ω              ⁢                                                          ⁢                              C                2                            ⁢                              R                0                                                                        (                  Equation          ⁢                                          ⁢          3                )                                FRF        =                                                      V              0                                      ω              2                                                                    (                  Equation          ⁢                                          ⁢          4                )                                          C          1                =                  -                                    2              ⁢                              d                33                            ⁢                              M                e                                      r                                              (                  Equation          ⁢                                          ⁢          5                )                                          C          2                =                  -                                    2              ⁢              π              ⁢                                                          ⁢              r              ⁢                                                          ⁢                              ɛ                33                                      h                                              (                  Equation          ⁢                                          ⁢          6                )                                          M          e                =                  2          -                                    2              ⁢              K                                                      2                ⁢                K                            -                                                m                  1                                ⁢                                  ω                  2                                                              +                                    2              ⁢              K                                                      2                ⁢                K                            -                                                m                  2                                ⁢                                  ω                  2                                                                                        (                  Equation          ⁢                                          ⁢          7                )            where r and h are the thickness and radius of the piezoelectric material. U0 represents the excitation amplitude and R0=10 KΩ is the resistive load.
FIG. 3 shows the analytically measured effective mass of such exemplary prior art embodiment as a function of wave frequency. Dynamic effective mass of the system is found negative at 0.42 KHz and 3.3 KHz. The effective mass becomes negative close to the local resonance frequency of the interior masses, which implies that wave energy is trapped inside and cannot be transmitted through the structure. Consequently, the embedded PZT generally 28 is stressed and maximum FRF is noticed at local resonance frequencies as depicted in prior art FIG. 3. Two FRF picks are observed, with the first pick resulting from the local resonance of the core mass and with the second pick due to the PZT resonance.
Analytically, numerically and experimentally obtained dynamic FRF for a resistive load of 10 KΩ are shown with FIG. 3, with analytically computed dynamic effective mass plotted at the bottom of such illustration. Therefore, prior art FIG. 3 confirms that the experimental approach underpins the analytical and numerical approaches as well with maximum potential at 0.37 KHz and 3.1 KHz. Because of instrumentation lapse and fabrication limitations, little shift of FRF picks is noticed in experimental studies. It was found that with such acousto-elastic metamaterial embodiment generally 20, up to 35 μW power was produced for a resistive load of 10 KΩ, which is significantly higher than the power generated (in nW range) by the above-referenced phononic crystal based energy harvesters.
Prior art FIG. 4 illustrates the harmonic excitation directions of a representative unit cell generally 30 to introduce different local resonance modes (P, Q, R, and S, respectively). Thus, FIG. 4 represents acquiring the local resonance modes with external loading (i.e., FIG. 4 represents the eigen modes of the unit cell 30). Different loading conditions are considered to actuate the different local resonance modes. Boundary displacement excitations are considered to acquire corresponding local resonance modes. Specifically, excitation along the Z- and X-axes result in designated P and Q modes, respectively. Harmonic rotation about Y- and Z-axes result in designated R and S modes, respectively.
Prior art FIG. 5 represents placement of piezoelectric wafers inside the soft core of the representative AESC 30 (see FIG. 4) for multi-modal harvesting below 1 kHz. The top row of the illustration shows plan views for modes P (32), Q (34), R(36), and S(38), respectively, while the bottom row shows the side views thereof.
Each resonance mode arrests the dynamic wave energy inside the matrix-resonator in unique ways inside the cell 30. Appropriate placement of an energy conversion material with proper design inside a matrix component capable of mechanoelectrical transduction (e.g. a piezoelectric material) can provide significant electric potential at the local resonance frequencies. Prior art FIG. 6 represents PZT placement of unit cell 30 to harvest energy from mode Q.
Considering such Q mode at about 415 Hz, since the center mass 26 resonates along the longitudinal direction of the cell 30, placing a piezoelectric disk in between the center mass 26 and aluminum frame 22 effectively harvests electrical potential. Piezoelectric wafer disk 28 is placed such that its thickness axis lies concurrent to the center line axis of the core mass 26, as illustrated in FIG. 6. Similar basic physics may be used to place other wafers for other modes as shown in FIG. 5.
Specific examples of harvesting the energy from the mode Q using the displacement excitation direction of the unit-cell AESC 30 is shown in the following article, which is fully incorporated herein by reference and for all purposes: “A Sub-Wavelength Scale Acoustoelastic Sonic Crystal for Harvesting Energies at very Low Frequencies (<˜1 KHz) using Controlled Geometric Configurations” published in the Journal of Intelligent Material Systems and Structures, Special Issue Article, DOI: 10.1177/1045389X16645863, Ahmed, R., Madisetti, D., Banerjee, S., (2016).
See also the following additional articles, which are fully incorporated herein by reference and for all purposes:    “Low Frequency Energy scavenging using sub-wave length scale acousto-elastic metamaterial”, AIP Advances, Vol. 4 (11), 10.1063/1.4901915, Ahmed, R., Banerjee, S., (2014); and    “Energy scavenging from acoustoelastic metamaterial using local resonance phenomenon”, Proc. SPIE 9431, Active and Passive Smart Structures and Integrated Systems 2015, 943106 (Apr. 2, 2015); doi:10.1117/12.2084773, Ahmed, R., Adiba, A., Banerjee, S., (2015).
In general, the AESC generally 30 consists of a relatively stiff frame 22 and a relatively heavy core 26 encapsulated into a soft matrix material 24. The piezoelectric material 28 is embedded into the matrix material 24 to convert the strain energy to electric potential. To convert the trapped strain energy into electrical potential at the selected mode Q, a piezoelectric wafer 28 (ϕ=about 7 mm, thickness=about 0.5 mm, mass=about 0.16 g) is embedded inside the matrix 24 in between the lead core 26 and the cavity wall 22 (FIG. 6) at a specific distance “h” from the core mass 26, which was found to be approximately H/4 to maximize the energy density, where “H” is the distance between core mass 26 and cavity wall 22. In the numerical study, a unit displacement of 1 mm is applied as the excitation input to evaluate the dynamic response of the AESC generally. For displacement excitation, the whole structure would need to be installed on a vibratory base. Displacement excitation technique was used for experimental validation and simplicity.
The AESC generally 30 was fabricated by placing the piezoelectric wafer 28 for the Q mode design as shown in FIG. 6. Machined aluminum 6061 was used as the boundary structure 22 with a cylindrical hole to place rubber 24 and lead 26 components. The diameter of lead ball 26 was slightly lower than the thickness of aluminum block 22. To place ball 26 at the middle (concerning all three dimensions) of the aluminum hole, a cylindrical support is designed and fabricated through 3D printing technology. The cylindrical support (not separately illustrated) consisted of three parts (insider, base, and handle) with the diameter of the insider portion as exactly the same as the diameter of the aluminum hole. A small arc indentation was used at the middle of the insider, to hold lead ball 26 at the middle. The insider was inside of the aluminum hole and its dimensions were set to support the lead core 26 at the middle of the structure with high precision. Diameter of the base is slightly higher than the width of the aluminum block 22, so that it carries the whole structure.
The fabrication process was divided into two steps. First, lead core 26 was placed inside the middle of aluminum block 22 using the cylindrical support. A liquid rubber (OOMOO 300, containing two parts, mixed slowly to avoid bubbles and to provide homogeneous strength) was used to fill the hole in aluminum block 22. Since it was necessary to sense/transfer signal from the rubber component, a piezoelectric disk 28 (with soldered wire) was fully submerged into the liquid rubber in such a way that it remained untouched with both lead ball 26 and aluminum structure 22. Usual rubber curing time was 6 hours. However, it is required to start the second step of fabrication at around 3 to 4 hours after the first step.
During the initial steps, cylindrical support was used to hold lead ball 26 at the middle. Hence, an empty space was open at the bottom of the structure after removing the cylindrical support. In the second step, such new empty space was filled with rubber following the same procedure described above. Since it is required to have a good bonding between the rubber, the second step was started before the full curing time in the first step.
FIG. 7A is a schematic diagram of the arrangement for measuring results with a unit cell metamaterial AESC embodiment 30 as referenced above, while FIG. 7B pictures equipment for the experimental arrangement, as shown schematically in FIG. 7A.
The Vibration Exciter generally 40 is a type 4809 from B & K Instruments, and was employed for managing harmonic displacement excitation. A sine-random Generator (type 1024) generally 42 and Power Amplifier (type 2706) generally 44 from Bruel & Kjaer were used to control excitation frequency. Voltage output generally 46 and 48 from wafer 28 was captured across a 10 KOhm resistive load generally 50, using oscilloscope 52. A support structure generally 54 was devised as represented to hold unit cell 30 for excitation by exciter equipment 40. Per the 2016 Ahmed et al. publication noted above, upon a unit displacement of 1 mm excitation, maximum power density of 92.4 mW/cm2 was recorded from the experimental results with such set-up. The set-up showed that energy could be harvested at four different frequencies using the AESC embodiment 30, with higher amounts of power generated over other existing harvesters. The set-up also showed that the local resonance frequencies of the AESC system of embodiment 30 were independent of their structural geometry, and that the AESC embodiment 30 is capable of simultaneously filtering acoustic waves and harvesting energy.
However, the presently disclosed subject matter addresses different loading conditions separately. More particularly, the presently disclosed subject matter addresses loading condition(s) to actuate all four available local resonance modes, or a particular environmental loading condition that could trigger all the possible modes of vibration, in equivalence, to harvest multi-modal energy with higher power density. Thus, while it has been shown that, four local resonance modes exist within a 1 kHz frequency level, the presently disclosed subject matter seeks to maximize potential power output of such arrangements. In other words, the presently disclosed subject matter seeks to optimize power for a unit cell metamaterial energy harvester.